Problem: Simplify the following expression and state the condition under which the simplification is valid. $p = \dfrac{n^2 - 36}{n + 6}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{36} = 6$ So we can rewrite the expression as: $p = \dfrac{({n} + {6})({n} {-6})} {n + 6} $ We can divide the numerator and denominator by $(n + 6)$ on condition that $n \neq -6$ Therefore $p = n - 6; n \neq -6$